arXiv Machine Learning
Persistent Cross Entropy
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Sep 2
Persistent Entropy as a Detector of Phase Transitions
The paper presents a model‑agnostic theorem that provides conditions under which a structural change in a persistence barcode leads to a detectable change in persistent entropy. By treating persistence diagrams as random objects indexed by a control parameter, the authors identify a dispersion‑condensation mechanism in the normalized persistence weights and derive an explicit lower bound on the entropy difference between two regimes, valid with high probability at finite sample size and independent of the absolute scale of bar lifetimes. The criterion is applied to convolutional networks, revealing a sharp topological phase transition in the circular organization of learned filters, and it also detects the Kuramoto synchronization and Vicsek order‑disorder transitions.
arXiv Machine Learning
Aug 7
Stochastic Dynamics on Persistence Diagram Space via Reinforcement Learning
arXiv:2608. 06276v1 Announce Type: cross Abstract: Persistence diagrams (PDs) provide stable and interpretable summaries of multiscale topological structure.
arXiv Machine Learning
Jun 11
From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features
arXiv:2606. 11911v1 Announce Type: cross Abstract: Persistence diagrams are common representations in topological data analysis, but they do not naturally live in a vector space, and the statistical tools developed for comparing them have largely evolved separately from those used for downstream prediction.
arXiv Machine Learning
Jul 24
Conditional Entropy of Heat Diffusion on Temporal Networks
arXiv:2605. 21514v2 Announce Type: replace-cross Abstract: Diffusion-based information-theoretic approaches provide new theoretical and practical tools to study complex networks.
arXiv Machine Learning
Sep 23
What Does Chain-of-Thought Entropy Measure? A Channel Audit of Scaffolding, Routing, and Content
The paper investigates how entropy over chain‑of‑thought tokens influences policy decisions such as gradient application, pruning, and collapse detection. By separating scaffold tokens from substantive content, the authors analyze entropy, Kullback–Leibler divergence, and entropy velocity for each channel, proving differences between raw and content conventions and bounding answer diversity. Empirical results across 23 configurations show that scaffold tokens can account for up to 41% of high‑entropy positions, with entropy share growing through distillation, while content conventions outperform raw surprisal on compression tasks and reveal significant answer leakage in re‑fed chains.
arXiv Machine Learning
Sep 1
Influence-Directed Distillation: Solving the Diversity Bottleneck in Sampled-Token On-Policy Distillation
arXiv:2608.29846v1 Announce Type: cross Abstract: Sampled-token on-policy distillation (OPD) efficiently transfers capabilities from teacher to student using student-generated tokens, requiring teach...